calculus/ Simpson's rule

Question

a. What is the third digit of your student ID number, from the left? For example, if your student ID is 7654321.

b. Consider the f(x) = kx^x and g(x) = -kx^x+2k. Take the digit you identified in the first question and substitute it for k.  Consider the region that is bounded by your f(x) and g(x). Use a graphing utility to graph and visualize your region and find where f(x) intercepts g(x).www.desmos.com/calculator.

c. According to your graphing utility, where do f(x) and g(x) intersect? Please provide these as (x,y) coordinates.

d. Consider your region in question 3 above. Set up the integral that describes you rotating the region you have identified in question 3 about the line x=7.

e. Make sure you include your bounds of integration in your integral. Use Simpson's rule to approximate your integral with n = 6.

Answer 1

the function is k x^k + kx^x - 2k = 2k x^k - 2k = 2k (x^x-1)

THe solution is (1,1), so the integral is from (0,1) and it blows up after that

Simpson's RUle says on (0,1) the area is Answer: -0.21653749055907

dont forget to multiply by K